Hilbert 双模作为辛对偶对的经典极限
Classical Limits of Hilbert Bimodules as Symplectic Dual Pairs
AI总结：
本文证明严格形变量子化不仅能从辛对偶对构造 Hilbert 双模，还能反向函子地取 Hilbert 双模的经典极限来重构辛对偶对。
摘要：
Hilbert 双模是量子系统的 C*-代数模型之间的态射，而辛对偶对是经典系统的 Poisson 几何模型之间的态射。这两类态射都保持相应类型模型的表示论结构。此前已有研究表明，可以通过严格形变量子化将某些辛对偶对函子地关联到 Hilbert 双模。我们证明，在相反方向上，严格形变量子化也允许人们函子地取 Hilbert 双模的经典极限，以重构一个辛对偶对。
英文摘要：
Hilbert bimodules are morphisms between C*-algebraic models of quantum systems, while symplectic dual pairs are morphisms between Poisson geometric models of classical systems. Both of these morphisms preserve representation-theoretic structures of the relevant types of models. Previously, it has been shown that one can functorially associate certain symplectic dual pairs to Hilbert bimodules through strict deformation quantization. We show that, in the inverse direction, strict deformation quantization also allows one to functorially take the classical limit of a Hilbert bimodule to reconstruct a symplectic dual pair.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
